关于l-路和图的超欧拉性  

On the Supereulerian Property of l-Path-Sum Graphs

作　　者：李晓璞 刘娟[1] LI Xiaopu;LIU Juan(College of Mathematical Sciences,Xinjiang Normal University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆师范大学数学科学学院,乌鲁木齐830017

出　　处：《西华师范大学学报（自然科学版）》2018年第3期271-275,共5页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11761071);新疆师范大学"十三五"校级重点学科数学招标课题资助项目(17SDKD1107)

摘　　要：令G_1和G_2是两个点不交的图,P1l和P2l分别是G_1和G_2中长为l的路,将P1l和P2l中的点分别对应重合,得到G_1和G_2-E P(2)l的并,称为G_1和G_2的l-路和,记作G_1P1l,P2lG_2。本文将介绍两个无向图的l-路和是超欧拉图、D-超欧拉图和T-超欧拉图的充分条件;以及特殊的,当l=1时,介绍两个无向图的2-和是超欧拉图、D-超欧拉图和T-超欧拉图的充分条件。通过对这些问题的讨论和证明,可以深入人们对关于超欧拉图在运算方面的认识和了解,以便在以后的研究和实际应用中更好地利用超欧拉的相关性质。Let G1 and G2 be two vertex disjoi spe ly. The ι-path-sum G1＋p1ι,p2ιG2 of G1 nt graphs,and then P1ι and P2ι are and G2 with base paths P1ι and P2ι two paths of length in G1 and G2 re- is obtained from the union of G1 and G2-E（P2ι） by identifying v2 and v2 for all j=[0,ι] respectively. In this paper, sufficient conditions in the ι-path- sum of supereulerian,D-supereulerian and T-supereulerian are introduced. Especially when I = 1, sufficient condi- tions in the 2-path-sum of supereulerian,D-supereulerian and T-supereulerian are also talked about. By discussing and proving these problems,it is hoped that the nature of Supereulerian graphs can be further understood and put into better use in the future.

关 键 词：l-路和 2-和 超欧拉图 D-超欧拉图 T-超欧拉图 

分 类 号：O157.5[理学—数学] O157.6[理学—基础数学]